Hvad er afstanden mellem de følgende polære koordinater ?: (7, (5pi) / 4), (2, (9pi) / 8)

Svar:

# P_1P_2 = sqrt (53-28cos ((pi) / 8)) ~ ~ 5.209 #

Forklaring:

# P_1P_2 = sqrt (r_1 ^ 2 + r_2 ^ 2-2r_1r_2cos (theta_2-theta_1)) #

# r_1 = 7, theta_1 = (5pi) / 4; r_2 = 2, theta_2 = (9pi) / 8 #

# P_1P_2 = sqrt (7 ^ 2 + 2 ^ 2-2 * 7 * 2cos (9pi) / 8- (5pi) / 4)) #

# P_1P_2 = sqrt (49 + 4-28cos (- (pi) / 8) #

# P_1P_2 = sqrt (53-28cos ((pi) / 8)) ~ ~ 5.209 #

Svar:

# S ~ = 5,27 #

Forklaring:

# R_1 = 7 #

# R_2 = 2 #

# Theta_1 = (5pi) / 4 #

# Theta_2 = (9pi) / 8 #

# Theta_2-theta_1 = (9pi) / 8- (5pi) / 4 = (9pi-10pi) / 8 = -pi / 8 #

#cos (-pi / 8) = 0,9 #

# S = sqrt (r_1 ^ 2 + r_2 ^ 2-2 * r_1 * r_2 * cos (theta_2-theta_1)) #

# S = sqrt (7 ^ 2 + 2 ^ 2-2 * 7 * 2 * 0,9) #

# S = sqrt (49 + 4-28 * 0,9) #

# S = sqrt (53-25,2) #

# S = sqrt (27,8) #

# s ~ = 5,27 #